hi recently noticed that my dog has been bitting his back like it itches him alot and theres fur lose and small black patches on his skin. the gooey looking thing is me applying lime sulfur cream on him which i think it irritated his skin so i clean it off as best i could and strayed anticeptic spray on it.

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It looks like he is deep into coat blow. Getting the old fur off quickly will help if debris is trapped under the dead coat that could be irritating patches. My white male is allergic to everything and getting his old coat off of him quickly once he starts to blow is paramount to his health. Once I have cleared the old coat then I bathe him in a medicated shampoo called Trizchlor4. It helps with itching and cleans the bacteria that the old coat was holding against the skin. You can find it on amazon. Once they have lost patches like that it takes a while for the fur to return if it even will. Staying up on brushing and skin hygiene will be important to getting the hair back. Identifying if he is allergic to something that caused the initial loss would be step two, especially if the hair doesn't start to come back once he is super clean and maintained.